1. **State the problem:** We need to find the limit of the function $f(x)$ as $x$ approaches $-3$, i.e., $\lim_{x \to -3} f(x)$. 2. **Recall the definition of a limit:** The limit $\lim_{x \to a} f(x)$ exists if and only if the left-hand limit $\lim_{x \to a^-} f(x)$ and the right-hand limit $\lim_{x \to a^+} f(x)$ both exist and are equal. 3. **Analyze the graph near $x = -3$:** - Look at the values of $f(x)$ as $x$ approaches $-3$ from the left side. - Look at the values of $f(x)$ as $x$ approaches $-3$ from the right side. 4. **Determine the left-hand limit:** From the graph, as $x$ approaches $-3$ from the left, $f(x)$ approaches a certain value (observe the y-value of the curve just before $x = -3$). 5. **Determine the right-hand limit:** From the graph, as $x$ approaches $-3$ from the right, $f(x)$ approaches a certain value (observe the y-value of the curve just after $x = -3$). 6. **Compare the two one-sided limits:** If they are equal, that value is the limit. If they differ, the limit does not exist (DNE). 7. **Check the function value at $x = -3$:** Note that the limit depends on the behavior near $-3$, not the actual function value at $-3$. 8. **Conclusion:** Based on the graph, the left-hand and right-hand limits as $x$ approaches $-3$ are equal to 2. Therefore, $$\lim_{x \to -3} f(x) = 2.$$